關於波動學的簡單物理問題

Tieria

2009-12-30 5:43 am

1. There shows a loudspeaker unit with two speaker cones, a big one and a small one. One speaker cone emits low-frequency sounds and the other emits high-frequency sounds. The sound waves generated by the speaker cones will bend around the rim of the cones in a way similar to water waves bending around corners of obstacles. Which cone is more suitable for emitting high-frequency sounds? Explain your answer. (4 marks)

Ans.:
The smaller speaker cone is more suitable for emitting high-frequency sounds. high-frequency sounds have shorter wavelengths. If the smaller cone is used, the sound waves will bend around the rim and diffract to the surroundings more significantly ( OR spread over a larger area).

問題：
在此，不是larger wavelength，diffraction才能更明顯，wavelength才能更comparable的嗎？

回答 (1)

天同

2009-12-30 6:14 am

✔ 最佳答案

A louspeaker cone has a circular opening. This phenomenon of "circular aperture diffraction" taks place.

The degree of diffraction at a circular opening depends, not only on the wavelength of the wave, but on the ratio of wavength to the diameter of the circular opening.

High frequency sounds do have shorter wavelength than low frequency sounds. In order to achieve prominent diffraction effect, the diameter of the cone has to be smaller such that the ratio of wavelength to cone diameter is high.

You could refer to the following web-page for a rigorous mathematical analysis of the problem. The equation at the end of the page is relevant.

http://cnx.org/content/m13097/latest/

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